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Simple Linear Regression (Slope) Calculator

Predicted change in Y for a 1-unit change in X.

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Slope (b)

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Overview

In simple linear regression, the slope coefficient represents the expected change in the dependent variable for every one-unit increase in the independent variable. This specific formula calculates the slope by adjusting the Pearson correlation coefficient based on the ratio of the variability in the outcome variable to the variability in the predictor.

Symbols

Variables

b = Slope (b), r = Correlation, SD_y = SD of Y, SD_x = SD of X

Slope (b)
Correlation
SD of Y
SD of X

Apply it well

When To Use

When to use: This formula is used when you need to establish a predictive relationship between two continuous variables and have already calculated their correlation and standard deviations. It is appropriate when the relationship between variables is linear and you wish to determine the unstandardized effect size in raw units.

Why it matters: In psychological research, understanding the slope allows clinicians and scientists to quantify the impact of variables, such as how much a patient's anxiety score might decrease for every hour of therapy completed. It provides a more practical, unit-based interpretation of data than correlation alone.

Avoid these traps

Common Mistakes

  • Swapping SDx and SDy.
  • Extrapolating outside the data range.

One free problem

Practice Problem

A psychologist finds that the correlation between weekly exercise hours (X) and subjective well-being scores (Y) is 0.50. If the standard deviation of well-being scores is 12 and the standard deviation of exercise hours is 2, calculate the regression slope.

Correlation0.5
SD of Y12
SD of X2

Solve for:

Hint: Divide the standard deviation of Y by the standard deviation of X, then multiply by the correlation.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Gravetter, F. J., Wallnau, L. B., Forzano, L. B. (2018). Statistics for the Behavioral Sciences (10th ed.). Cengage Learning.
  2. Wikipedia: Simple linear regression
  3. Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). SAGE Publications.
  4. Gravetter, F. J., Wallnau, L. B., Forzano, L. B., & Witnauer, J. E. (2021). Essentials of statistics for the behavioral sciences (10th ed.).
  5. Wikipedia: Pearson correlation coefficient
  6. Wikipedia: Standard deviation
  7. Howell, D. C. (2013). Statistical Methods for Psychology (8th ed.). Wadsworth Cengage Learning.
  8. University Psychology — Statistics